Preliminary NPB Model for Adiposity
Sheena Martenies
07/20/2020
This version of the adiposity analysis mirrors the birth weight analysis from 09_NPB_Model_BW_v3_MD.R
Some key findings to note:
- There are fewer participants with complete data on the adiposity outcome and covariates of interest
1 Exploring the data set
The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.
The complete data set for the adiposity outcome consists of n = 780 participants. This represents 67.77% of the original Healthy Start 1 cohort.
Of the 780 participants, 0.26% identify as Latina, 0.17% identify as Black, and 0.26% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 0.51% of babies born were male.
1.1 Exposure data
We have included 19 exposures in our analysis.
These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3), these are based on long-term averages at for each census tract. For mean_pm and mean_o3 are based on the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 8.483046 47.19072 6.006276 43.30893 10128.4962
## [2,] 6.598608 50.05090 7.281109 48.36432 10749.0359
## [3,] 7.454146 48.57052 17.205991 31.67281 9048.6468
## [4,] 6.671239 50.06429 6.842898 45.00359 4223.3434
## [5,] 7.122537 50.14275 3.357792 28.16745 858.7283
## [6,] 7.637453 47.03125 10.743612 45.87564 15603.9800
## dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] 2827.538 729.2371 4829.780 7968.654 29116.58
## [2,] 1576.420 5239.2211 4417.792 3780.951 51044.30
## [3,] 3350.303 2992.2968 5211.871 7423.232 36079.21
## [4,] 3364.954 6998.1286 8921.318 9636.816 42235.78
## [5,] 2923.811 3427.2247 7006.042 6806.912 29145.98
## [6,] 3364.200 3166.5395 4484.960 5265.285 43921.85
## dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,] 1749.1256 275.2480 155.7767 14.377133
## [2,] 7354.5310 279.6435 226.8038 8.905404
## [3,] 4887.2996 221.0414 157.6974 7.636888
## [4,] 3752.6399 203.8812 142.5368 2.850212
## [5,] 729.7784 194.1983 101.0046 5.435988
## [6,] 5870.6867 174.3361 120.3281 5.035971
## property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,] 37.32935 31.784946 11.529628 26.114650 12.010919
## [2,] 67.03932 15.290231 4.908306 8.500401 18.123496
## [3,] 46.78194 6.891702 4.564963 0.000000 6.307978
## [4,] 21.95270 2.725915 5.623583 1.350621 9.292274
## [5,] 22.49834 12.919186 5.234103 6.307385 2.115768
## [6,] 47.15500 3.842365 10.000000 5.121799 25.171768
## pct_poc
## [1,] 90.33703
## [2,] 30.44025
## [3,] 26.63305
## [4,] 32.68648
## [5,] 73.60772
## [6,] 23.08698Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 pct_tree_cover
## mean_pm 0.387935651 -0.006062324 -0.24186797
## mean_o3 -0.006062324 8.955071063 -0.42975173
## pct_tree_cover -0.241867968 -0.429751728 10.14239201
## pct_impervious 0.374669222 -1.022666581 7.01532904
## mean_aadt_intensity -244.348900205 303.692966735 9016.25164719
## dist_m_tri -262.436608185 331.077954338 -208.41963901
## dist_m_npl -323.917936386 588.917794378 165.47445225
## dist_m_waste_site -255.868380544 139.101947771 1967.86242644
## dist_m_major_emit 54.696478097 795.943835213 109.80052618
## dist_m_cafo -1416.446418998 -161.908280851 10579.76974425
## dist_m_mine_well -346.805134977 -503.738613039 3305.89212551
## cvd_rate_adj 3.764074301 4.075840732 -24.37524733
## res_rate_adj 1.965274289 1.428149656 -1.41491470
## violent_crime_rate 0.155877411 0.749569861 -3.73949960
## property_crime_rate 1.705778861 -1.922286944 -21.72665992
## pct_less_hs 1.150349004 1.853281484 -7.56529205
## pct_unemp 0.055091002 0.506543293 -0.09840703
## pct_limited_eng 0.412512233 1.029344921 -2.79407307
## pct_hh_pov 0.606596961 0.246447334 0.62423227
## pct_poc 1.697984717 3.441448054 -19.39024560
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.3746692 -244.3489 -262.4366
## mean_o3 -1.0226666 303.6930 331.0780
## pct_tree_cover 7.0153290 9016.2516 -208.4196
## pct_impervious 179.3785613 56186.2650 -16125.7853
## mean_aadt_intensity 56186.2649588 69165922.5363 -1545741.2032
## dist_m_tri -16125.7853155 -1545741.2032 6796986.1348
## dist_m_npl -9073.4066413 1215685.3718 4579262.3957
## dist_m_waste_site -5149.3668557 1813109.3670 2501094.5398
## dist_m_major_emit 2552.7325419 2477044.2166 1636072.5435
## dist_m_cafo 17731.4297754 15642123.4910 3145985.3646
## dist_m_mine_well 1088.8996239 2146886.0916 937920.3657
## cvd_rate_adj 238.2585184 20288.9695 -51713.8246
## res_rate_adj 182.9073227 34962.3596 -32708.1468
## violent_crime_rate 23.5426763 4766.3910 -848.4942
## property_crime_rate 96.9554914 18227.6819 -3222.6487
## pct_less_hs 59.7110274 -3644.3902 -12701.6695
## pct_unemp 25.7808764 5880.6527 -2452.4569
## pct_limited_eng 42.8626714 2701.0340 -5437.8035
## pct_hh_pov 84.0422503 18597.5270 -8881.9880
## pct_poc 89.6891621 4493.4912 -18654.6550
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -323.9179 -255.8684 54.69648
## mean_o3 588.9178 139.1019 795.94384
## pct_tree_cover 165.4745 1967.8624 109.80053
## pct_impervious -9073.4066 -5149.3669 2552.73254
## mean_aadt_intensity 1215685.3718 1813109.3670 2477044.21655
## dist_m_tri 4579262.3957 2501094.5398 1636072.54352
## dist_m_npl 11347069.4851 4199731.9447 7041775.87881
## dist_m_waste_site 4199731.9447 5299321.7913 1350703.22559
## dist_m_major_emit 7041775.8788 1350703.2256 10385263.63290
## dist_m_cafo 4931146.1458 5617993.1230 -3395813.15490
## dist_m_mine_well 258232.8698 1384614.0282 -1787310.96945
## cvd_rate_adj -33265.8693 -43188.0097 15096.48910
## res_rate_adj -19718.2591 -31937.2229 -1526.60012
## violent_crime_rate -152.7587 -3204.3439 461.39386
## property_crime_rate -14876.4444 -19362.3191 -20045.85330
## pct_less_hs -6945.0281 -11539.8973 8548.88251
## pct_unemp 2139.2957 -1457.5039 5159.73353
## pct_limited_eng 432.5398 -4292.4445 9331.34328
## pct_hh_pov -1451.6169 -7730.1917 8680.72868
## pct_poc -2074.8078 -8515.4005 21998.02980
## dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -1416.4464 -346.8051 3.764074 1.965274
## mean_o3 -161.9083 -503.7386 4.075841 1.428150
## pct_tree_cover 10579.7697 3305.8921 -24.375247 -1.414915
## pct_impervious 17731.4298 1088.8996 238.258518 182.907323
## mean_aadt_intensity 15642123.4910 2146886.0916 20288.969539 34962.359641
## dist_m_tri 3145985.3646 937920.3657 -51713.824619 -32708.146822
## dist_m_npl 4931146.1458 258232.8698 -33265.869348 -19718.259098
## dist_m_waste_site 5617993.1230 1384614.0282 -43188.009668 -31937.222912
## dist_m_major_emit -3395813.1549 -1787310.9695 15096.489101 -1526.600117
## dist_m_cafo 46839423.7820 9553723.7226 -44601.199501 -7797.531774
## dist_m_mine_well 9553723.7226 4464054.8852 -38076.395520 -14953.132358
## cvd_rate_adj -44601.1995 -38076.3955 2076.657134 1315.804108
## res_rate_adj -7797.5318 -14953.1324 1315.804108 1110.806026
## violent_crime_rate 408.3455 -2058.0613 134.891314 100.535111
## property_crime_rate -18380.9466 -4567.0382 320.604924 290.157212
## pct_less_hs -24463.8379 -9889.2545 334.637464 201.489440
## pct_unemp -416.0610 -2620.4519 105.334428 74.963887
## pct_limited_eng -6285.3923 -4618.3890 185.226339 106.490953
## pct_hh_pov 252.0453 -4667.4525 269.033064 206.556606
## pct_poc -42540.4506 -24578.3527 619.542560 300.056264
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.1558774 1.705779 1.150349
## mean_o3 0.7495699 -1.922287 1.853281
## pct_tree_cover -3.7394996 -21.726660 -7.565292
## pct_impervious 23.5426763 96.955491 59.711027
## mean_aadt_intensity 4766.3910356 18227.681901 -3644.390223
## dist_m_tri -848.4941529 -3222.648703 -12701.669456
## dist_m_npl -152.7586849 -14876.444381 -6945.028107
## dist_m_waste_site -3204.3438644 -19362.319083 -11539.897288
## dist_m_major_emit 461.3938611 -20045.853299 8548.882507
## dist_m_cafo 408.3455047 -18380.946611 -24463.837868
## dist_m_mine_well -2058.0613390 -4567.038163 -9889.254521
## cvd_rate_adj 134.8913140 320.604924 334.637464
## res_rate_adj 100.5351114 290.157212 201.489440
## violent_crime_rate 36.5195077 135.346154 25.285073
## property_crime_rate 135.3461545 1160.236223 3.004961
## pct_less_hs 25.2850735 3.004961 163.762734
## pct_unemp 12.0566338 3.018063 40.254624
## pct_limited_eng 14.1433364 -11.409839 86.491751
## pct_hh_pov 30.5537434 63.667397 103.102830
## pct_poc 52.0085020 -26.369164 241.514049
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.05509100 0.4125122 0.6065970 1.697985
## mean_o3 0.50654329 1.0293449 0.2464473 3.441448
## pct_tree_cover -0.09840703 -2.7940731 0.6242323 -19.390246
## pct_impervious 25.78087638 42.8626714 84.0422503 89.689162
## mean_aadt_intensity 5880.65274910 2701.0340348 18597.5269669 4493.491248
## dist_m_tri -2452.45686782 -5437.8034938 -8881.9879579 -18654.655039
## dist_m_npl 2139.29571806 432.5397585 -1451.6169481 -2074.807832
## dist_m_waste_site -1457.50390263 -4292.4445272 -7730.1916796 -8515.400484
## dist_m_major_emit 5159.73353103 9331.3432771 8680.7286763 21998.029803
## dist_m_cafo -416.06100829 -6285.3922771 252.0452517 -42540.450615
## dist_m_mine_well -2620.45185414 -4618.3890431 -4667.4524666 -24578.352704
## cvd_rate_adj 105.33442831 185.2263391 269.0330637 619.542560
## res_rate_adj 74.96388699 106.4909525 206.5566058 300.056264
## violent_crime_rate 12.05663378 14.1433364 30.5537434 52.008502
## property_crime_rate 3.01806326 -11.4098394 63.6673970 -26.369164
## pct_less_hs 40.25462427 86.4917511 103.1028300 241.514049
## pct_unemp 24.70089342 25.8002340 37.9257486 73.691783
## pct_limited_eng 25.80023399 69.4638469 69.0402541 143.757101
## pct_hh_pov 37.92574856 69.0402541 122.9753676 158.037277
## pct_poc 73.69178348 143.7571008 158.0372769 530.391699ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 1.63895222 -0.2235917 -0.09106707 0.2355128 -0.004372722
## [2,] -1.38658135 0.7321879 0.30923073 0.6129716 0.070241827
## [3,] -0.01298527 0.2374938 3.42564459 -0.6332930 -0.134215290
## [4,] -1.26996939 0.7366655 0.17163233 0.3620440 -0.714416377
## [5,] -0.54539411 0.7628814 -0.92269126 -0.8950193 -1.118982302
## [6,] 0.28132089 -0.2768817 1.39645679 0.4271554 0.654006942
## dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] -0.3966655 -1.41524068 -0.158944386 -0.09829063 -1.1211055
## [2,] -0.8765539 -0.07638689 -0.337912010 -1.39776302 2.0828583
## [3,] -0.1961498 -0.74341877 0.007035929 -0.26753873 -0.1037626
## [4,] -0.1905302 0.44577016 1.618419775 0.41935153 0.7958031
## [5,] -0.3597382 -0.61430417 0.786424074 -0.45878682 -1.1168106
## [6,] -0.1908194 -0.69169232 -0.308734136 -0.93716429 1.0421630
## dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,] -0.7694006 0.6888535 -0.2667071 0.2857705
## [2,] 1.8836300 0.7853085 1.8643986 -0.6196746
## [3,] 0.7158928 -0.5006603 -0.2090789 -0.8295849
## [4,] 0.1788599 -0.8772257 -0.6639585 -1.6216694
## [5,] -1.2518563 -1.0897090 -1.9100974 -1.1937830
## [6,] 1.1813285 -1.5255654 -1.3303122 -1.2599766
## property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,] -0.5116110 1.20006290 0.38269452 2.15729293 -0.2815741
## [2,] 0.3606149 -0.08889067 -0.94956352 0.04387831 0.2696336
## [3,] -0.2341017 -0.74518055 -1.01864671 -0.97602734 -0.7958425
## [4,] -0.9630391 -1.07070943 -0.80564470 -0.81397542 -0.5267306
## [5,] -0.9470203 -0.27417225 -0.88401077 -0.21924683 -1.1738791
## [6,] -0.2231493 -0.98346622 0.07492226 -0.36149732 0.9052185
## pct_poc
## [1,] 1.5763100
## [2,] -1.0244789
## [3,] -1.1897923
## [4,] -0.9269452
## [5,] 0.8499036
## [6,] -1.3437665Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 pct_tree_cover pct_impervious
## mean_pm 1.000000000 -0.003252556 -0.121934980 0.04491412
## mean_o3 -0.003252556 1.000000000 -0.045093393 -0.02551610
## pct_tree_cover -0.121934980 -0.045093393 1.000000000 0.16447223
## pct_impervious 0.044914121 -0.025516099 0.164472230 1.00000000
## mean_aadt_intensity -0.047172018 0.012202649 0.340415825 0.50442756
## dist_m_tri -0.161616753 0.042436304 -0.025102111 -0.46182497
## dist_m_npl -0.154387912 0.058422253 0.015424777 -0.20111444
## dist_m_waste_site -0.178454140 0.020192428 0.268419703 -0.16701613
## dist_m_major_emit 0.027250266 0.082535188 0.010698563 0.05914408
## dist_m_cafo -0.332287904 -0.007905490 0.485400532 0.19344287
## dist_m_mine_well -0.263536583 -0.079672044 0.491307868 0.03848024
## cvd_rate_adj 0.132616005 0.029888236 -0.167956353 0.39037390
## res_rate_adj 0.094672580 0.014319244 -0.013330331 0.40975731
## violent_crime_rate 0.041413399 0.041449103 -0.194303596 0.29087615
## property_crime_rate 0.080402522 -0.018858645 -0.200285524 0.21252691
## pct_less_hs 0.144325222 0.048394870 -0.185629913 0.34838683
## pct_unemp 0.017796906 0.034058516 -0.006217268 0.38730765
## pct_limited_eng 0.079465308 0.041271190 -0.105266007 0.38398526
## pct_hh_pov 0.087823617 0.007426438 0.017675307 0.56585263
## pct_poc 0.118373795 0.049935378 -0.264371573 0.29077451
## mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm -0.04717202 -0.16161675 -0.154387912
## mean_o3 0.01220265 0.04243630 0.058422253
## pct_tree_cover 0.34041583 -0.02510211 0.015424777
## pct_impervious 0.50442756 -0.46182497 -0.201114438
## mean_aadt_intensity 1.00000000 -0.07129064 0.043394356
## dist_m_tri -0.07129064 1.00000000 0.521429359
## dist_m_npl 0.04339436 0.52142936 1.000000000
## dist_m_waste_site 0.09470388 0.41673672 0.541588668
## dist_m_major_emit 0.09242275 0.19473123 0.648681599
## dist_m_cafo 0.27481716 0.17631641 0.213894809
## dist_m_mine_well 0.12217945 0.17027191 0.036283143
## cvd_rate_adj 0.05353422 -0.43527735 -0.216707839
## res_rate_adj 0.12613498 -0.37642515 -0.175633598
## violent_crime_rate 0.09483772 -0.05385527 -0.007504152
## property_crime_rate 0.06434461 -0.03628955 -0.129653449
## pct_less_hs -0.03424296 -0.38071069 -0.161110784
## pct_unemp 0.14227321 -0.18927221 0.127782869
## pct_limited_eng 0.03896768 -0.25025681 0.015406527
## pct_hh_pov 0.20165084 -0.30721536 -0.038859849
## pct_poc 0.02346062 -0.31069243 -0.026744696
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.17845414 0.02725027 -0.332287904
## mean_o3 0.02019243 0.08253519 -0.007905490
## pct_tree_cover 0.26841970 0.01069856 0.485400532
## pct_impervious -0.16701613 0.05914408 0.193442865
## mean_aadt_intensity 0.09470388 0.09242275 0.274817163
## dist_m_tri 0.41673672 0.19473123 0.176316410
## dist_m_npl 0.54158867 0.64868160 0.213894809
## dist_m_waste_site 1.00000000 0.18207111 0.356586819
## dist_m_major_emit 0.18207111 1.00000000 -0.153967569
## dist_m_cafo 0.35658682 -0.15396757 1.000000000
## dist_m_mine_well 0.28467794 -0.26249836 0.660696709
## cvd_rate_adj -0.41169031 0.10279803 -0.143007353
## res_rate_adj -0.41626308 -0.01421338 -0.034184739
## violent_crime_rate -0.23033849 0.02369194 0.009873237
## property_crime_rate -0.24693009 -0.18261758 -0.078847675
## pct_less_hs -0.39172768 0.20729701 -0.279325946
## pct_unemp -0.12739232 0.32215300 -0.012231928
## pct_limited_eng -0.22372532 0.34742094 -0.110191273
## pct_hh_pov -0.30281059 0.24290606 0.003320960
## pct_poc -0.16061887 0.29639895 -0.269896936
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.26353658 0.13261601 0.09467258
## mean_o3 -0.07967204 0.02988824 0.01431924
## pct_tree_cover 0.49130787 -0.16795635 -0.01333033
## pct_impervious 0.03848024 0.39037390 0.40975731
## mean_aadt_intensity 0.12217945 0.05353422 0.12613498
## dist_m_tri 0.17027191 -0.43527735 -0.37642515
## dist_m_npl 0.03628314 -0.21670784 -0.17563360
## dist_m_waste_site 0.28467794 -0.41169031 -0.41626308
## dist_m_major_emit -0.26249836 0.10279803 -0.01421338
## dist_m_cafo 0.66069671 -0.14300735 -0.03418474
## dist_m_mine_well 1.00000000 -0.39546556 -0.21234806
## cvd_rate_adj -0.39546556 1.00000000 0.86634271
## res_rate_adj -0.21234806 0.86634271 1.00000000
## violent_crime_rate -0.16118740 0.48982295 0.49915588
## property_crime_rate -0.06345950 0.20654495 0.25558834
## pct_less_hs -0.36575582 0.57383181 0.47241713
## pct_unemp -0.24954857 0.46508423 0.45256051
## pct_limited_eng -0.26226862 0.48768672 0.38336652
## pct_hh_pov -0.19920768 0.53237076 0.55887015
## pct_poc -0.50511428 0.59032393 0.39091760
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.041413399 0.08040252 0.14432522
## mean_o3 0.041449103 -0.01885865 0.04839487
## pct_tree_cover -0.194303596 -0.20028552 -0.18562991
## pct_impervious 0.290876145 0.21252691 0.34838683
## mean_aadt_intensity 0.094837724 0.06434461 -0.03424296
## dist_m_tri -0.053855270 -0.03628955 -0.38071069
## dist_m_npl -0.007504152 -0.12965345 -0.16111078
## dist_m_waste_site -0.230338488 -0.24693009 -0.39172768
## dist_m_major_emit 0.023691938 -0.18261758 0.20729701
## dist_m_cafo 0.009873237 -0.07884767 -0.27932595
## dist_m_mine_well -0.161187402 -0.06345950 -0.36575582
## cvd_rate_adj 0.489822949 0.20654495 0.57383181
## res_rate_adj 0.499155881 0.25558834 0.47241713
## violent_crime_rate 1.000000000 0.65752195 0.32695970
## property_crime_rate 0.657521947 1.00000000 0.00689379
## pct_less_hs 0.326959697 0.00689379 1.00000000
## pct_unemp 0.401427649 0.01782784 0.63292450
## pct_limited_eng 0.280808338 -0.04019082 0.81093815
## pct_hh_pov 0.455924473 0.16855235 0.72653072
## pct_poc 0.373691766 -0.03361436 0.81947649
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.017796906 0.07946531 0.087823617 0.11837380
## mean_o3 0.034058516 0.04127119 0.007426438 0.04993538
## pct_tree_cover -0.006217268 -0.10526601 0.017675307 -0.26437157
## pct_impervious 0.387307652 0.38398526 0.565852631 0.29077451
## mean_aadt_intensity 0.142273206 0.03896768 0.201650845 0.02346062
## dist_m_tri -0.189272211 -0.25025681 -0.307215358 -0.31069243
## dist_m_npl 0.127782869 0.01540653 -0.038859849 -0.02674470
## dist_m_waste_site -0.127392321 -0.22372532 -0.302810585 -0.16061887
## dist_m_major_emit 0.322153000 0.34742094 0.242906063 0.29639895
## dist_m_cafo -0.012231928 -0.11019127 0.003320960 -0.26989694
## dist_m_mine_well -0.249548573 -0.26226862 -0.199207679 -0.50511428
## cvd_rate_adj 0.465084229 0.48768672 0.532370759 0.59032393
## res_rate_adj 0.452560508 0.38336652 0.558870145 0.39091760
## violent_crime_rate 0.401427649 0.28080834 0.455924473 0.37369177
## property_crime_rate 0.017827843 -0.04019082 0.168552353 -0.03361436
## pct_less_hs 0.632924498 0.81093815 0.726530718 0.81947649
## pct_unemp 1.000000000 0.62285635 0.688127265 0.64381987
## pct_limited_eng 0.622856353 1.00000000 0.746988474 0.74894777
## pct_hh_pov 0.688127265 0.74698847 1.000000000 0.61880258
## pct_poc 0.643819872 0.74894777 0.618802578 1.00000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.2 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
NOTE: It’ll be interesting to see what comes out of our BEAMERS discussion re: adjusting for gestational age. It’s currently in the analysis
There are four continuous covariates; all of the others have been coded as dummy variables. For the dummy variables, the reference groups are: white_re, ed_grad, norm_bmi
W <- select(hs_data2,
lat, lon, lat_lon_int,
latina_re, black_re, other_re,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w, days_to_peapod) %>%
as.matrix()
head(W)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133 -4170.944 1 0 0 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [4,] 39.68397 -104.8933 -4162.583 0 0 0 0 0
## [5,] 39.79134 -104.7669 -4168.814 0 1 0 0 0
## [6,] 39.68050 -104.9451 -4164.274 1 0 0 0 0
## ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 1 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 1 0
## [5,] 0 1 0 0 0 1 0
## [6,] 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 19
## [2,] 0 1 0 0 0 36
## [3,] 0 1 0 0 0 34
## [4,] 0 1 0 0 0 28
## [5,] 0 1 0 0 0 30
## [6,] 0 1 0 0 0 22
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w days_to_peapod
## [1,] 0 1 29 0 0 40.57143 1
## [2,] 0 0 19 2 1 35.85714 2
## [3,] 0 0 19 1 0 40.42857 2
## [4,] 0 0 20 0 0 36.28571 1
## [5,] 0 0 15 0 1 38.42857 2
## [6,] 0 0 17 1 0 40.71429 1Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "gest_age_w" "days_to_peapod"W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27, 28)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:20], W.s[,4],
W[,22:23], W.s[,5:6],
W[,26], W.s[,7:8])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "" "gest_age_w" "days_to_peapod"colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,] 0.9582490 0.5369709 -0.5836483 1 0 0 0
## [2,] -1.5595136 -1.6096907 0.6608980 0 0 1 0
## [3,] 0.2858292 -0.6547167 -0.4971411 0 0 0 0
## [4,] -0.6978905 -0.4200223 0.4143032 0 0 0 0
## [5,] 0.9178908 1.0931096 -0.3293688 0 1 0 0
## [6,] -0.7500299 -1.0397812 0.2123849 1 0 0 0
## ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 0 1 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 1 0
## [5,] 0 0 1 0 0 0 1 0
## [6,] 0 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 -1.41994612
## [2,] 0 1 0 0 0 1.35302672
## [3,] 0 1 0 0 0 1.02679462
## [4,] 0 1 0 0 0 0.04809832
## [5,] 0 1 0 0 0 0.37433042
## [6,] 0 1 0 0 0 -0.93059797
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w days_to_peapod
## [1,] 0 1 3.3968005 -1.3157360 0 0.8044835 -0.2392302
## [2,] 0 0 0.1208193 -0.6918928 1 -2.7388783 0.1867962
## [3,] 0 0 0.1208193 -1.0038144 0 0.6971089 0.1867962
## [4,] 0 0 0.4484174 -1.3157360 0 -2.4167545 -0.2392302
## [5,] 0 0 -1.1895732 -1.3157360 1 -0.8061355 0.1867962
## [6,] 0 0 -0.5343769 -1.0038144 0 0.9118581 -0.2392302summary(W.scaled)## lat lon lat_lon_int latina_re
## Min. :-2.46715 Min. :-2.4830 Min. :-3.510301 Min. :0.0000
## 1st Qu.:-0.62450 1st Qu.:-0.5811 1st Qu.:-0.493286 1st Qu.:0.0000
## Median : 0.05945 Median : 0.1064 Median : 0.008488 Median :0.0000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.000000 Mean :0.2628
## 3rd Qu.: 0.43089 3rd Qu.: 0.6643 3rd Qu.: 0.599123 3rd Qu.:1.0000
## Max. : 4.01365 Max. : 4.5155 Max. : 2.628224 Max. :1.0000
## black_re other_re ed_no_hs ed_hs
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.1654 Mean :0.06667 Mean :0.1538 Mean :0.1833
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## ed_aa ed_4yr low_bmi ovwt_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.0000
## Mean :0.2256 Mean :0.2205 Mean :0.03077 Mean :0.2615
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.0000
## obese_bmi concep_spring concep_summer concep_fall
## Min. :0.0000 Min. :0.0000 Min. :0.00 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.00 Median :0.0000
## Mean :0.1962 Mean :0.2436 Mean :0.25 Mean :0.2667
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.25 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.00 Max. :1.0000
## concep_2010 concep_2011 concep_2012 concep_2013
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1692 Mean :0.2936 Mean :0.2808 Mean :0.2551
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## maternal_age any_smoker smokeSH mean_cpss
## Min. :-1.9093 Min. :0.00000 Min. :0.0000 Min. :-6.10355
## 1st Qu.:-0.9306 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:-0.53438
## Median : 0.0481 Median :0.00000 Median :0.0000 Median : 0.01162
## Mean : 0.0000 Mean :0.08718 Mean :0.2474 Mean : 0.00000
## 3rd Qu.: 0.7006 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.: 0.55762
## Max. : 2.6580 Max. :1.00000 Max. :1.0000 Max. : 3.39680
## mean_epsd male gest_age_w days_to_peapod
## Min. :-1.3157 Min. :0.0000 Min. :-5.20849 Min. :-0.6653
## 1st Qu.:-0.7959 1st Qu.:0.0000 1st Qu.:-0.48401 1st Qu.:-0.2392
## Median :-0.1720 Median :1.0000 Median : 0.05286 Median :-0.2392
## Mean : 0.0000 Mean :0.5064 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.5558 3rd Qu.:1.0000 3rd Qu.: 0.69711 3rd Qu.:-0.2392
## Max. : 3.9869 Max. :1.0000 Max. : 3.81097 Max. :10.4114Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int latina_re
## lat 1.0000000000 -0.2294265015 -0.922594810 0.01488040464
## lon -0.2294265015 1.0000000000 0.587147326 0.00774099102
## lat_lon_int -0.9225948101 0.5871473257 1.000000000 -0.00928638293
## latina_re 0.0148804046 0.0077409910 -0.009286383 0.19399460189
## black_re -0.0076765642 0.0416993781 0.022926625 -0.04352226721
## other_re 0.0022244292 -0.0045513219 -0.003662305 -0.01754385965
## ed_no_hs -0.0002536098 0.0211421973 0.008600587 0.03781968994
## ed_hs -0.0092915161 0.0376437998 0.022660243 0.03262729996
## ed_aa -0.0072973858 0.0461167337 0.024355069 0.01250781739
## ed_4yr 0.0084748321 -0.0053108878 -0.009175293 -0.03620683980
## low_bmi -0.0031399188 0.0031935883 0.003878110 -0.00167868075
## ovwt_bmi 0.0176550362 0.0102854255 -0.010619251 0.02488397354
## obese_bmi 0.0151602612 0.0074254851 -0.009652703 0.02283499556
## concep_spring 0.0203171932 -0.0022492530 -0.017790516 -0.00633619697
## concep_summer -0.0229599220 -0.0001995618 0.019015261 -0.00417201540
## concep_fall 0.0095582094 0.0161897319 -0.001540859 0.01583226359
## concep_2010 0.0109529805 0.0028301792 -0.008007944 -0.00859089563
## concep_2011 -0.0226544797 0.0224924333 0.027745587 -0.01050821237
## concep_2012 0.0015394008 -0.0023870971 -0.002215499 0.01340475955
## concep_2013 0.0089319968 -0.0236248234 -0.016772917 0.00474803331
## maternal_age 0.0348578763 -0.1930103076 -0.105532928 -0.11130236864
## any_smoker -0.0069992076 0.0222429459 0.014635045 -0.00753760574
## smokeSH 0.0011347413 0.0442610839 0.016595995 -0.00349725157
## mean_cpss -0.0279187887 -0.0046586574 0.021381618 -0.04032749691
## mean_epsd -0.0458873302 0.0573784314 0.060923471 0.03908431534
## male 0.0224103855 -0.0245595335 -0.028364840 0.00152233304
## gest_age_w 0.0302744587 -0.0833518477 -0.058256588 -0.00772944439
## days_to_peapod 0.0166177524 -0.0037582676 -0.015297436 -0.00006310256
## black_re other_re ed_no_hs ed_hs
## lat -0.0076765642 0.0022244292 -0.0002536098 -0.0092915161
## lon 0.0416993781 -0.0045513219 0.0211421973 0.0376437998
## lat_lon_int 0.0229266248 -0.0036623054 0.0086005874 0.0226602429
## latina_re -0.0435222672 -0.0175438596 0.0378196899 0.0326273000
## black_re 0.1382097363 -0.0110397946 0.0143181594 0.0158536585
## other_re -0.0110397946 0.0623020967 -0.0025673941 0.0031664527
## ed_no_hs 0.0143181594 -0.0025673941 0.1303446233 -0.0282413350
## ed_hs 0.0158536585 0.0031664527 -0.0282413350 0.1499144202
## ed_aa 0.0178335144 0.0041934104 -0.0347585662 -0.0414206247
## ed_4yr -0.0172607880 -0.0031664527 -0.0339685988 -0.0404792469
## low_bmi 0.0026068925 -0.0007702182 -0.0034561074 -0.0005134788
## ovwt_bmi 0.0003357362 -0.0059050064 0.0046410586 -0.0069319641
## obese_bmi 0.0073121359 0.0023106547 0.0057272638 0.0268934531
## concep_spring -0.0005431026 0.0055626872 -0.0028636319 0.0014976466
## concep_summer -0.0067394095 0.0000000000 -0.0038510911 -0.0060975610
## concep_fall -0.0069319641 -0.0023962345 0.0102695764 0.0062473256
## concep_2010 0.0117705145 -0.0010269576 0.0008887133 0.0074454429
## concep_2011 0.0155672953 -0.0003423192 0.0112570356 -0.0063970903
## concep_2012 -0.0118346993 -0.0007702182 -0.0047398045 0.0062259307
## concep_2013 -0.0152908068 0.0022250749 -0.0072084527 -0.0070389388
## maternal_age -0.0914960717 -0.0135406562 -0.1473311448 -0.1061266380
## any_smoker 0.0150883776 -0.0006846384 0.0173792831 0.0045357296
## smokeSH 0.0321961094 0.0065896448 0.0324874099 0.0251818571
## mean_cpss -0.0362044396 0.0225734779 -0.0574356146 -0.0356451617
## mean_epsd 0.0160927464 0.0210839610 0.0715352956 0.0221439428
## male -0.0055544584 0.0021394951 -0.0151081268 0.0007488233
## gest_age_w -0.0459673981 -0.0051550835 -0.0121190054 -0.0148312028
## days_to_peapod 0.0353079864 0.0037188443 0.0068992133 0.0014765999
## ed_aa ed_4yr low_bmi ovwt_bmi
## lat -0.007297386 0.0084748321 -0.0031399188 0.0176550362
## lon 0.046116734 -0.0053108878 0.0031935883 0.0102854255
## lat_lon_int 0.024355069 -0.0091752931 0.0038781104 -0.0106192507
## latina_re 0.012507817 -0.0362068398 -0.0016786808 0.0248839735
## black_re 0.017833514 -0.0172607880 0.0026068925 0.0003357362
## other_re 0.004193410 -0.0031664527 -0.0007702182 -0.0059050064
## ed_no_hs -0.034758566 -0.0339685988 -0.0034561074 0.0046410586
## ed_hs -0.041420625 -0.0404792469 -0.0005134788 -0.0069319641
## ed_aa 0.174951450 -0.0498206116 0.0046015602 0.0179322603
## ed_4yr -0.049820612 0.1721075672 -0.0003752345 0.0013034462
## low_bmi 0.004601560 -0.0003752345 0.0298607682 -0.0080576676
## ovwt_bmi 0.017932260 0.0013034462 -0.0080576676 0.1933840229
## obese_bmi 0.012165498 -0.0137849314 -0.0060432507 -0.0513676311
## concep_spring 0.006583062 -0.0062868240 -0.0049372963 0.0068134689
## concep_summer -0.010269576 0.0089858793 0.0038510911 -0.0051347882
## concep_fall -0.010183997 0.0014548567 0.0033376123 0.0046213094
## concep_2010 0.002843883 0.0011454528 0.0024883974 -0.0032388664
## concep_2011 0.002988710 0.0057799282 0.0025081465 0.0065567295
## concep_2012 -0.005668016 -0.0067937198 -0.0047990520 -0.0054902735
## concep_2013 -0.001158619 0.0001514104 -0.0001579935 0.0025081465
## maternal_age -0.034152305 0.1077776102 -0.0091971230 0.0067327450
## any_smoker 0.008544814 -0.0153977815 0.0011652019 -0.0048582996
## smokeSH 0.021118462 -0.0353773740 0.0026463908 -0.0108818011
## mean_cpss 0.029189204 0.0275174804 0.0079977462 -0.0043164323
## mean_epsd 0.016391602 -0.0481925954 0.0107834260 0.0098080614
## male 0.001119121 0.0062868240 -0.0001974919 -0.0029623778
## gest_age_w -0.025824190 0.0330362179 -0.0033335217 -0.0159296533
## days_to_peapod 0.025249438 -0.0107106080 -0.0073703791 -0.0139751139
## obese_bmi concep_spring concep_summer concep_fall
## lat 0.015160261 0.0203171932 -0.0229599220 0.0095582094
## lon 0.007425485 -0.0022492530 -0.0001995618 0.0161897319
## lat_lon_int -0.009652703 -0.0177905156 0.0190152613 -0.0015408589
## latina_re 0.022834996 -0.0063361970 -0.0041720154 0.0158322636
## black_re 0.007312136 -0.0005431026 -0.0067394095 -0.0069319641
## other_re 0.002310655 0.0055626872 0.0000000000 -0.0023962345
## ed_no_hs 0.005727264 -0.0028636319 -0.0038510911 0.0102695764
## ed_hs 0.026893453 0.0014976466 -0.0060975610 0.0062473256
## ed_aa 0.012165498 0.0065830618 -0.0102695764 -0.0101839966
## ed_4yr -0.013784931 -0.0062868240 0.0089858793 0.0014548567
## low_bmi -0.006043251 -0.0049372963 0.0038510911 0.0033376123
## ovwt_bmi -0.051367631 0.0068134689 -0.0051347882 0.0046213094
## obese_bmi 0.157879925 -0.0029130048 -0.0054557125 -0.0048780488
## concep_spring -0.002913005 0.1844903064 -0.0609756098 -0.0650406504
## concep_summer -0.005455712 -0.0609756098 0.1877406932 -0.0667522465
## concep_fall -0.004878049 -0.0650406504 -0.0667522465 0.1958065896
## concep_2010 -0.004996544 -0.0233040387 0.0012836970 0.0267008986
## concep_2011 0.002671077 0.0041308713 -0.0003209243 -0.0129225503
## concep_2012 0.009040190 -0.0119976301 0.0016046213 0.0033376123
## concep_2013 -0.006462921 0.0314834930 -0.0022464698 -0.0167736414
## maternal_age -0.002069755 0.0029368513 0.0128775828 -0.0263135433
## any_smoker 0.003416609 -0.0007241368 0.0012836970 -0.0014548567
## smokeSH 0.011735953 -0.0051512458 -0.0093068036 -0.0005990586
## mean_cpss -0.017623185 0.0102636126 0.0090765847 -0.0058688239
## mean_epsd 0.021537334 -0.0093232881 -0.0185691459 0.0210706139
## male 0.000666535 -0.0028471742 -0.0073812580 -0.0017115961
## gest_age_w -0.018839063 -0.0120553886 -0.0012405281 0.0303791551
## days_to_peapod 0.003874497 0.0061840510 -0.0155863326 -0.0080939552
## concep_2010 concep_2011 concep_2012 concep_2013
## lat 0.0109529805 -0.0226544797 0.0015394008 0.0089319968
## lon 0.0028301792 0.0224924333 -0.0023870971 -0.0236248234
## lat_lon_int -0.0080079439 0.0277455872 -0.0022154991 -0.0167729167
## latina_re -0.0085908956 -0.0105082124 0.0134047596 0.0047480333
## black_re 0.0117705145 0.0155672953 -0.0118346993 -0.0152908068
## other_re -0.0010269576 -0.0003423192 -0.0007702182 0.0022250749
## ed_no_hs 0.0008887133 0.0112570356 -0.0047398045 -0.0072084527
## ed_hs 0.0074454429 -0.0063970903 0.0062259307 -0.0070389388
## ed_aa 0.0028438827 0.0029887100 -0.0056680162 -0.0011586189
## ed_4yr 0.0011454528 0.0057799282 -0.0067937198 0.0001514104
## low_bmi 0.0024883974 0.0025081465 -0.0047990520 -0.0001579935
## ovwt_bmi -0.0032388664 0.0065567295 -0.0054902735 0.0025081465
## obese_bmi -0.0049965439 0.0026710773 0.0090401896 -0.0064629209
## concep_spring -0.0233040387 0.0041308713 -0.0119976301 0.0314834930
## concep_summer 0.0012836970 -0.0003209243 0.0016046213 -0.0022464698
## concep_fall 0.0267008986 -0.0129225503 0.0033376123 -0.0167736414
## concep_2010 0.1407721931 -0.0497481979 -0.0475757875 -0.0432309667
## concep_2011 -0.0497481979 0.2076610381 -0.0825367829 -0.0749991771
## concep_2012 -0.0475757875 -0.0825367829 0.2021970969 -0.0717241039
## concep_2013 -0.0432309667 -0.0749991771 -0.0717241039 0.1902817550
## maternal_age -0.0328905868 -0.0432339945 0.0317389331 0.0462084289
## any_smoker 0.0031993680 0.0090319608 -0.0078206774 -0.0042987393
## smokeSH 0.0094203614 0.0145535038 -0.0182136862 -0.0067262434
## mean_cpss 0.0079265785 -0.0141064917 -0.0086484999 0.0104679503
## mean_epsd -0.0144672243 0.0406582459 -0.0297416911 0.0052396759
## male 0.0014811889 -0.0050936441 0.0014071295 0.0028554030
## gest_age_w -0.0066182705 -0.0045846526 0.0012150814 0.0089551286
## days_to_peapod -0.0279586414 -0.0014177042 -0.0328007113 0.0624841560
## maternal_age any_smoker smokeSH mean_cpss
## lat 0.034857876 -0.0069992076 0.0011347413 -0.027918789
## lon -0.193010308 0.0222429459 0.0442610839 -0.004658657
## lat_lon_int -0.105532928 0.0146350446 0.0165959949 0.021381618
## latina_re -0.111302369 -0.0075376057 -0.0034972516 -0.040327497
## black_re -0.091496072 0.0150883776 0.0321961094 -0.036204440
## other_re -0.013540656 -0.0006846384 0.0065896448 0.022573478
## ed_no_hs -0.147331145 0.0173792831 0.0324874099 -0.057435615
## ed_hs -0.106126638 0.0045357296 0.0251818571 -0.035645162
## ed_aa -0.034152305 0.0085448142 0.0211184622 0.029189204
## ed_4yr 0.107777610 -0.0153977815 -0.0353773740 0.027517480
## low_bmi -0.009197123 0.0011652019 0.0026463908 0.007997746
## ovwt_bmi 0.006732745 -0.0048582996 -0.0108818011 -0.004316432
## obese_bmi -0.002069755 0.0034166091 0.0117359534 -0.017623185
## concep_spring 0.002936851 -0.0007241368 -0.0051512458 0.010263613
## concep_summer 0.012877583 0.0012836970 -0.0093068036 0.009076585
## concep_fall -0.026313543 -0.0014548567 -0.0005990586 -0.005868824
## concep_2010 -0.032890587 0.0031993680 0.0094203614 0.007926578
## concep_2011 -0.043233995 0.0090319608 0.0145535038 -0.014106492
## concep_2012 0.031738933 -0.0078206774 -0.0182136862 -0.008648500
## concep_2013 0.046208429 -0.0042987393 -0.0067262434 0.010467950
## maternal_age 1.000000000 -0.0452178456 -0.1497337791 0.111663918
## any_smoker -0.045217846 0.0796813798 0.0490043119 0.012438902
## smokeSH -0.149733779 0.0490043119 0.1864504131 0.022013301
## mean_cpss 0.111663918 0.0124389018 0.0220133014 1.000000000
## mean_epsd -0.170707705 0.0453127030 0.1111391210 0.441020650
## male 0.026063884 0.0020078338 0.0016210790 -0.007214721
## gest_age_w 0.073088144 -0.0297069373 -0.0509973685 -0.007275391
## days_to_peapod -0.001591990 -0.0022885196 0.0107316422 -0.005995421
## mean_epsd male gest_age_w days_to_peapod
## lat -0.045887330 0.0224103855 0.030274459 0.01661775239
## lon 0.057378431 -0.0245595335 -0.083351848 -0.00375826760
## lat_lon_int 0.060923471 -0.0283648398 -0.058256588 -0.01529743598
## latina_re 0.039084315 0.0015223330 -0.007729444 -0.00006310256
## black_re 0.016092746 -0.0055544584 -0.045967398 0.03530798637
## other_re 0.021083961 0.0021394951 -0.005155083 0.00371884427
## ed_no_hs 0.071535296 -0.0151081268 -0.012119005 0.00689921335
## ed_hs 0.022143943 0.0007488233 -0.014831203 0.00147659993
## ed_aa 0.016391602 0.0011191205 -0.025824190 0.02524943813
## ed_4yr -0.048192595 0.0062868240 0.033036218 -0.01071060804
## low_bmi 0.010783426 -0.0001974919 -0.003333522 -0.00737037914
## ovwt_bmi 0.009808061 -0.0029623778 -0.015929653 -0.01397511387
## obese_bmi 0.021537334 0.0006665350 -0.018839063 0.00387449725
## concep_spring -0.009323288 -0.0028471742 -0.012055389 0.00618405099
## concep_summer -0.018569146 -0.0073812580 -0.001240528 -0.01558633260
## concep_fall 0.021070614 -0.0017115961 0.030379155 -0.00809395517
## concep_2010 -0.014467224 0.0014811889 -0.006618270 -0.02795864142
## concep_2011 0.040658246 -0.0050936441 -0.004584653 -0.00141770421
## concep_2012 -0.029741691 0.0014071295 0.001215081 -0.03280071127
## concep_2013 0.005239676 0.0028554030 0.008955129 0.06248415603
## maternal_age -0.170707705 0.0260638841 0.073088144 -0.00159199026
## any_smoker 0.045312703 0.0020078338 -0.029706937 -0.00228851955
## smokeSH 0.111139121 0.0016210790 -0.050997369 0.01073164223
## mean_cpss 0.441020650 -0.0072147212 -0.007275391 -0.00599542077
## mean_epsd 1.000000000 -0.0104804641 -0.086750438 0.01124930187
## male -0.010480464 0.2502797801 -0.039081937 0.03073094727
## gest_age_w -0.086750438 -0.0390819370 1.000000000 -0.13525838557
## days_to_peapod 0.011249302 0.0307309473 -0.135258386 1.00000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Response data: adiposty (%fat mass)
Y <- select(hs_data2, adiposity) %>%
as.matrix()
head(Y)## adiposity
## [1,] 9.217429
## [2,] 7.736959
## [3,] 13.474442
## [4,] 10.058402
## [5,] 11.836774
## [6,] 15.544041Distribution of adiposity and scaled adiposity
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
1.4 Scatterplots of exposures and outcome (adiposity)
Both adiposity (Y) and the exposures are scaled here
NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori
df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
lm.x <- lm(adiposity ~ df[,x], data = df)
plot(df[,c(x, 1)],
xlab = paste0(colnames(df)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULL2 Is gestational age a potenital mediator?
I.e., is there a relationship between our exposures and gestational age?
The DAG might look something like this:
exposures —> gestational age —> adiposity _________________________________^
2.1 Scatter plots for exposures and gestational age
Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery
Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.
df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
plot(df2[,c(x, 1)],
xlab = paste0(colnames(df2)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULLDropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "gest_age_w" "days_to_peapod"W.scaled2 <- W.scaled[,-c(ncol(W.scaled)-1)]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "days_to_peapod"3 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 28.18383#' Fit the model using the best_lambda
ad_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(ad_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 20 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(ad_ridge)## 21 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 9.70558400602256
## mean_pm -0.02918998917658
## mean_o3 -0.00162273345759
## pct_tree_cover -0.00707858012865
## pct_impervious -0.00123913479050
## mean_aadt_intensity 0.00000009893812
## dist_m_tri 0.00000265205071
## dist_m_npl 0.00000212103152
## dist_m_waste_site 0.00001231150399
## dist_m_major_emit 0.00000345442313
## dist_m_cafo -0.00000151278368
## dist_m_mine_well -0.00000771268856
## cvd_rate_adj -0.00040306658209
## res_rate_adj -0.00083778715037
## violent_crime_rate -0.00225734349381
## property_crime_rate -0.00082078900373
## pct_less_hs -0.00020033888696
## pct_unemp -0.00455074179190
## pct_limited_eng 0.00165523913246
## pct_hh_pov -0.00198488819875
## pct_poc 0.00033884831986Ridge regression predictions
ridge_pred <- predict(ad_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.01. Based on these results, it doesn’t look like there’s much here.
4 Nonparametric Bayesian Shrinkage (NPB): Adiposity
Still, we wanted to try to fit the NPB model with these data.
4.1 Finding the NPB priors
I’m starting with the sets of priors used in the birth weight analysis. Note: I’m including far fewer iterations of the priors than in the previous version of the document.
4.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0002244638 0.03065891 0.00000000 0.0000000 0.022
## [2,] -0.0067958594 0.04315122 -0.11098145 0.0000000 0.040
## [3,] -0.0008083469 0.01719508 0.00000000 0.0000000 0.024
## [4,] -0.0017197218 0.01517309 0.00000000 0.0000000 0.016
## [5,] 0.0028260054 0.03283555 0.00000000 0.0000000 0.020
## [6,] -0.0012387698 0.01700948 0.00000000 0.0000000 0.018
## [7,] -0.0022919297 0.02029178 0.00000000 0.0000000 0.024
## [8,] 0.0120896780 0.07253021 0.00000000 0.2618768 0.046
## [9,] -0.0002699095 0.01684193 0.00000000 0.0000000 0.014
## [10,] -0.0012055379 0.05334396 -0.02153362 0.0000000 0.030
## [11,] -0.0038794699 0.02685319 -0.05108612 0.0000000 0.034
## [12,] -0.0044363973 0.03007248 -0.07547669 0.0000000 0.036
## [13,] -0.0047005066 0.02977325 -0.09291597 0.0000000 0.046
## [14,] -0.0026175677 0.02044266 0.00000000 0.0000000 0.020
## [15,] -0.0121813286 0.04984710 -0.19301230 0.0000000 0.072
## [16,] -0.0029962666 0.02356645 0.00000000 0.0000000 0.028
## [17,] -0.0050847531 0.02860052 -0.09098849 0.0000000 0.036
## [18,] -0.0023298020 0.01995217 -0.03393439 0.0000000 0.034
## [19,] -0.0052407963 0.03149169 -0.09802491 0.0000000 0.040
## [20,] -0.0032854285 0.02067841 -0.04574963 0.0000000 0.028plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
4.1.2 Adjust alpha.pi and beta.pi
For now, leave a.phi1 and sig2inv.mu1 alone for now.
alpha.pi and beta.pi are responisble for the exclusion probability distribution. If we thing we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value
4.1.2.1 Try making alpha.pi and beta.pi 2
plot(density(rbeta(10000, 2, 2)))
priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0008128463 0.03124739 -0.045426603 0.00000000 0.056
## [2,] -0.0109923737 0.05491148 -0.188489076 0.00000000 0.080
## [3,] -0.0012359181 0.02669459 -0.044244016 0.00000000 0.050
## [4,] -0.0016687622 0.02705344 -0.057107448 0.00000000 0.056
## [5,] 0.0035674066 0.03439731 0.000000000 0.01238072 0.050
## [6,] -0.0045888455 0.02966178 -0.080787479 0.00000000 0.054
## [7,] -0.0014623699 0.01508674 0.000000000 0.00000000 0.032
## [8,] 0.0128235902 0.07731286 -0.009077207 0.28821531 0.078
## [9,] 0.0003622225 0.03485964 -0.033825431 0.00000000 0.052
## [10,] -0.0069302298 0.06327613 -0.142188896 0.00000000 0.076
## [11,] -0.0067992179 0.03816478 -0.125524049 0.00000000 0.074
## [12,] -0.0066837066 0.04192488 -0.129441981 0.00000000 0.078
## [13,] -0.0077043807 0.03757038 -0.122125837 0.00000000 0.072
## [14,] -0.0054648574 0.03264103 -0.109504269 0.00000000 0.062
## [15,] -0.0217930149 0.07215156 -0.271541695 0.00000000 0.132
## [16,] -0.0071413917 0.03840063 -0.134233049 0.00000000 0.062
## [17,] -0.0121014969 0.05691746 -0.162052752 0.00000000 0.072
## [18,] -0.0008698144 0.02599417 -0.043015340 0.00000000 0.058
## [19,] -0.0097883543 0.05050330 -0.133665258 0.00000000 0.074
## [20,] -0.0011165392 0.02251249 -0.015092778 0.00000000 0.040plot(fit.npb.12$beta[,1], type = "l")
plot(fit.npb.12$beta[,2], type = "l")
plot(fit.npb.12$beta[,13], type = "l")
4.1.2.2 Try making alpha.pi and beta.pi 5
plot(density(rbeta(10000, 5, 5)))
priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0100391500 0.04058843 -0.13728609 0.013267286 0.174
## [2,] -0.0311859775 0.09213937 -0.26277390 0.015386575 0.292
## [3,] -0.0067509157 0.04136229 -0.14205888 0.038934495 0.190
## [4,] -0.0101389914 0.03955327 -0.14086250 0.027123622 0.204
## [5,] -0.0002972584 0.04043334 -0.07729877 0.064741092 0.170
## [6,] -0.0074013398 0.04128202 -0.13728609 0.033609749 0.174
## [7,] -0.0058340326 0.03155346 -0.11077735 0.020271451 0.166
## [8,] 0.0179548429 0.09093975 -0.05469514 0.335231954 0.184
## [9,] -0.0037851039 0.02545463 -0.08254335 0.022396935 0.130
## [10,] -0.0175285140 0.06858538 -0.21628723 0.029974338 0.252
## [11,] -0.0250479003 0.07014295 -0.23944156 0.020271451 0.266
## [12,] -0.0195000190 0.05692325 -0.18818772 0.006343339 0.238
## [13,] -0.0201877423 0.05403820 -0.20158552 0.006218584 0.240
## [14,] -0.0128061241 0.04761605 -0.16126539 0.011007052 0.204
## [15,] -0.0461864279 0.08968315 -0.29500794 0.001394794 0.360
## [16,] -0.0188574365 0.05846165 -0.20019070 0.001778855 0.230
## [17,] -0.0295499716 0.08043544 -0.28515681 0.000000000 0.246
## [18,] -0.0061240400 0.03870974 -0.10508979 0.007924296 0.174
## [19,] -0.0149240850 0.04859332 -0.17037055 0.015386575 0.222
## [20,] -0.0056698357 0.04565578 -0.12725984 0.030992398 0.180plot(fit.npb.13$beta[,1], type = "l")
plot(fit.npb.13$beta[,2], type = "l")
plot(fit.npb.13$beta[,13], type = "l")
4.1.2.3 Try making alpha.pi and beta.pi 8
plot(density(rbeta(10000, 8, 8)))
priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.0157696404 0.05447552 -0.15739908 0.04315442 0.276
## [2,] -0.0295029568 0.07686046 -0.24874160 0.08394220 0.396
## [3,] -0.0121124911 0.05220660 -0.14452240 0.05045757 0.256
## [4,] -0.0166617178 0.05371270 -0.16163881 0.02241358 0.242
## [5,] 0.0052419830 0.05321659 -0.08229548 0.16517177 0.194
## [6,] -0.0171402228 0.05459742 -0.15161805 0.03931312 0.252
## [7,] -0.0057918603 0.03381693 -0.10635877 0.04204706 0.192
## [8,] 0.0263437385 0.10106607 -0.06271938 0.37720331 0.236
## [9,] 0.0001177643 0.04926960 -0.09959640 0.13982299 0.194
## [10,] -0.0127356580 0.09023425 -0.22158768 0.14588132 0.308
## [11,] -0.0350484822 0.07639394 -0.25187356 0.01714852 0.352
## [12,] -0.0179969693 0.05881989 -0.19021602 0.04022551 0.290
## [13,] -0.0283373799 0.06755326 -0.24525294 0.01712042 0.326
## [14,] -0.0114105676 0.07067475 -0.15015841 0.07270539 0.296
## [15,] -0.0670070386 0.11688415 -0.38054144 0.00000000 0.456
## [16,] -0.0253082592 0.09129863 -0.24399241 0.04609970 0.300
## [17,] -0.0398855660 0.08887281 -0.31011867 0.01740361 0.360
## [18,] -0.0045569685 0.05756825 -0.12005709 0.09556167 0.256
## [19,] -0.0260463966 0.06471700 -0.19534249 0.00000000 0.290
## [20,] -0.0077528761 0.05531862 -0.12638982 0.03686140 0.226plot(fit.npb.14$beta[,1], type = "l")
plot(fit.npb.14$beta[,2], type = "l")
plot(fit.npb.14$beta[,13], type = "l")
4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1
Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1
4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1
priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 1)
fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.010776076 0.05349721 -0.15983725 0.07186679 0.272
## [2,] -0.023840033 0.08083899 -0.22343347 0.06865878 0.316
## [3,] -0.006297729 0.05256468 -0.14040269 0.11545590 0.268
## [4,] -0.008872432 0.04551965 -0.14155830 0.08393444 0.238
## [5,] 0.005228278 0.05885120 -0.07828619 0.13906800 0.230
## [6,] -0.011272841 0.05409252 -0.16617134 0.08191122 0.264
## [7,] -0.004263896 0.04741990 -0.12623117 0.11406338 0.216
## [8,] 0.024492471 0.09102470 -0.07647902 0.29000886 0.272
## [9,] 0.001442495 0.04810147 -0.09193480 0.10594137 0.214
## [10,] -0.023658106 0.13556533 -0.27858483 0.09359547 0.340
## [11,] -0.026124365 0.07440119 -0.24393261 0.05356252 0.334
## [12,] -0.021586576 0.05904021 -0.18693920 0.04710151 0.326
## [13,] -0.025288324 0.06889897 -0.21201483 0.03397377 0.302
## [14,] -0.011316598 0.05236428 -0.16085115 0.06053328 0.242
## [15,] -0.062182020 0.10466476 -0.36330743 0.00659731 0.450
## [16,] -0.016349837 0.05699490 -0.19670489 0.06822506 0.258
## [17,] -0.040071602 0.09331811 -0.35274180 0.03896274 0.354
## [18,] -0.004190913 0.05497043 -0.13770796 0.11981376 0.234
## [19,] -0.022784679 0.06929598 -0.22197851 0.05161263 0.294
## [20,] -0.008090274 0.05739451 -0.16064309 0.05268181 0.214plot(fit.npb.23$beta[,1], type = "l")
plot(fit.npb.23$beta[,2], type = "l")
plot(fit.npb.23$beta[,13], type = "l")
4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.009324775 0.05481546 -0.15870289 0.07171425 0.272
## [2,] -0.035583946 0.09421746 -0.31208158 0.04528158 0.350
## [3,] -0.007146591 0.04943767 -0.14444216 0.06060265 0.248
## [4,] -0.015610240 0.05471313 -0.17028088 0.04364996 0.262
## [5,] 0.012446920 0.06739039 -0.07168868 0.23653155 0.250
## [6,] -0.007264592 0.05030023 -0.12902314 0.09232996 0.276
## [7,] -0.003154088 0.05249611 -0.10978735 0.10618214 0.242
## [8,] 0.042408726 0.11367189 -0.07477517 0.38840638 0.330
## [9,] 0.003285676 0.04793397 -0.08662208 0.14483082 0.232
## [10,] -0.017012527 0.11174794 -0.21958051 0.22669031 0.332
## [11,] -0.033230221 0.08430399 -0.29177495 0.06087094 0.366
## [12,] -0.025971443 0.06970725 -0.23669704 0.04451830 0.330
## [13,] -0.030943847 0.08218177 -0.29875486 0.04360241 0.322
## [14,] -0.008967903 0.05721818 -0.13945038 0.10916408 0.274
## [15,] -0.064553616 0.10748442 -0.36395187 0.00000000 0.440
## [16,] -0.016568711 0.05996401 -0.17755417 0.05133096 0.272
## [17,] -0.040174596 0.09055339 -0.30403167 0.01090636 0.352
## [18,] -0.002386577 0.05535941 -0.11369403 0.12042576 0.226
## [19,] -0.035366803 0.09786180 -0.28907058 0.05309944 0.356
## [20,] -0.002455106 0.05923952 -0.12332655 0.12806381 0.266plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
plot(fit.npb.24$beta[,15], type = "l")
4.2 Fit the NPB model
As with the birth weight model, I’ve used the 24th set of priors and set scaleY = T in the NPB model below
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "pct_tree_cover"
## [4] "pct_impervious" "mean_aadt_intensity" "dist_m_tri"
## [7] "dist_m_npl" "dist_m_waste_site" "dist_m_major_emit"
## [10] "dist_m_cafo" "dist_m_mine_well" "cvd_rate_adj"
## [13] "res_rate_adj" "violent_crime_rate" "property_crime_rate"
## [16] "pct_less_hs" "pct_unemp" "pct_limited_eng"
## [19] "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "days_to_peapod"# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Adiposity_v3.rdata"))
load(here::here("Results", "NPB_Adiposity_v3.rdata"))
npb.sum <- summary(fit.npb)4.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum$main.effects) <- colnames(X.scaled)
npb.sum$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -0.009521478 0.05821512 -0.15830691 0.10684002 0.3116
## mean_o3 -0.030065414 0.08499379 -0.28834910 0.06087740 0.3612
## pct_tree_cover -0.006925560 0.05544297 -0.14394429 0.09929996 0.2824
## pct_impervious -0.011747909 0.05126717 -0.14572875 0.06744699 0.2900
## mean_aadt_intensity 0.007088029 0.05965890 -0.08273797 0.18528231 0.2648
## dist_m_tri -0.010895546 0.05857536 -0.16787708 0.09608965 0.3036
## dist_m_npl -0.002794456 0.04977971 -0.11776067 0.10745454 0.2628
## dist_m_waste_site 0.033156529 0.10837580 -0.07790025 0.39905857 0.3172
## dist_m_major_emit 0.001631657 0.05553538 -0.10690768 0.14252991 0.2584
## dist_m_cafo -0.015783270 0.11410095 -0.24385825 0.15703486 0.3328
## dist_m_mine_well -0.027086077 0.07251168 -0.23691818 0.06002946 0.3652
## cvd_rate_adj -0.020069284 0.06390855 -0.19854017 0.05690473 0.3148
## res_rate_adj -0.024984788 0.06857139 -0.22057351 0.04218614 0.3408
## violent_crime_rate -0.015349772 0.05718232 -0.17417776 0.05789069 0.3024
## property_crime_rate -0.064508052 0.11463374 -0.39703779 0.02707757 0.4808
## pct_less_hs -0.018611264 0.06656410 -0.19998674 0.06008295 0.3160
## pct_unemp -0.039610700 0.09020572 -0.32858144 0.02475102 0.3800
## pct_limited_eng 0.001481397 0.06073486 -0.10731547 0.15831849 0.2664
## pct_hh_pov -0.027219328 0.07633254 -0.24312458 0.04018555 0.3424
## pct_poc -0.002740457 0.05712510 -0.12356143 0.13039102 0.2772npb.sum$main.effects$exp <- rownames(npb.sum$main.effects)## Warning in npb.sum$main.effects$exp <- rownames(npb.sum$main.effects): Coercing
## LHS to a listwrite_csv(as.data.frame(npb.sum$main.effects), here::here("Results", "NPB_Main_Effects_Adiposity.csv"))
#' Which one's have PIPs > 0.5
# selected_exp <- which(npb.sum$main.effects[,5] >= 0.5)
# selected_exp4.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum$covariates)[2:nrow(npb.sum$covariates)] <- colnames(W.scaled2)
npb.sum$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 9.12406987 1.6680749 5.80050128 12.3998817
## lat 0.13476071 2.4008347 -4.55616902 4.8932236
## lon 0.19547923 1.1633703 -2.08731118 2.4776199
## lat_lon_int 0.11924728 2.8926855 -5.53755126 5.8925294
## latina_re -0.33820110 0.3968317 -1.12378844 0.4377753
## black_re -0.17517825 0.4412733 -1.04874587 0.6465654
## other_re -0.85144707 0.5854248 -1.98113276 0.2880662
## ed_no_hs 1.20157334 0.6613282 -0.10998342 2.4931252
## ed_hs 1.07814739 0.5847854 -0.08671733 2.2466952
## ed_aa 0.87836711 0.5228787 -0.12981240 1.9054506
## ed_4yr 0.14363659 0.4261516 -0.68935698 0.9774243
## low_bmi -0.41884658 0.7913332 -1.92438276 1.1873734
## ovwt_bmi 0.48511019 0.3452160 -0.19794344 1.1511576
## obese_bmi 1.28949695 0.3900094 0.51019482 2.0532613
## concep_spring 0.29330544 0.4004486 -0.49706591 1.0894850
## concep_summer 0.05399113 0.4228442 -0.78793865 0.8663376
## concep_fall -0.03972963 0.4118140 -0.82730536 0.7855900
## concep_2010 0.28373271 1.6661177 -2.98599892 3.5271817
## concep_2011 -0.20830586 1.6369899 -3.41753890 2.9896781
## concep_2012 -0.48866354 1.6379308 -3.68191994 2.8022940
## concep_2013 -0.19864251 1.6456171 -3.40684030 3.0949784
## maternal_age 0.74452913 0.1839050 0.38630551 1.0946425
## any_smoker -0.87919935 0.5336508 -1.92993506 0.1644408
## smokeSH -0.08761295 0.3743784 -0.80873527 0.6175326
## mean_cpss -0.03248356 0.1622048 -0.35900187 0.2734223
## mean_epsd -0.20377764 0.1706113 -0.53158803 0.1327660
## male -1.36297276 0.2792668 -1.88951778 -0.7886671
## days_to_peapod 0.83264526 0.1417825 0.55172826 1.1109173npb.sum$covariates$exp <- rownames(npb.sum$covariates)## Warning in npb.sum$covariates$exp <- rownames(npb.sum$covariates): Coercing LHS
## to a listwrite_csv(as.data.frame(npb.sum$covariates), here::here("Results", "NPB_Covariates_Adiposity.csv"))4.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.000714816335 0.018705637 0.000000000 0 0.0060
## [2,] -0.000709420029 0.010064647 0.000000000 0 0.0080
## [3,] -0.002678101635 0.023422750 0.000000000 0 0.0180
## [4,] -0.000302982235 0.005240192 0.000000000 0 0.0056
## [5,] -0.000567884373 0.009659061 0.000000000 0 0.0092
## [6,] -0.000487813821 0.007500479 0.000000000 0 0.0064
## [7,] -0.004171511437 0.029329812 -0.035988587 0 0.0268
## [8,] -0.002289342406 0.022176267 0.000000000 0 0.0160
## [9,] -0.001285642778 0.015935178 0.000000000 0 0.0104
## [10,] -0.001332104520 0.014898732 0.000000000 0 0.0120
## [11,] -0.001204675266 0.014287677 0.000000000 0 0.0120
## [12,] -0.000354660216 0.008338736 0.000000000 0 0.0064
## [13,] -0.000434038738 0.006454505 0.000000000 0 0.0064
## [14,] -0.000122558194 0.005132664 0.000000000 0 0.0064
## [15,] -0.001841345005 0.017656567 0.000000000 0 0.0164
## [16,] -0.002144475243 0.020332125 0.000000000 0 0.0156
## [17,] -0.003182674834 0.027740483 0.000000000 0 0.0204
## [18,] -0.000553766044 0.008478782 0.000000000 0 0.0080
## [19,] -0.001668649713 0.017562827 0.000000000 0 0.0136
## [20,] -0.000445826172 0.007132295 0.000000000 0 0.0056
## [21,] -0.000249481048 0.006420783 0.000000000 0 0.0060
## [22,] 0.000181260526 0.010773276 0.000000000 0 0.0060
## [23,] -0.002138987498 0.019864111 0.000000000 0 0.0176
## [24,] -0.000827733741 0.010805316 0.000000000 0 0.0084
## [25,] -0.000737277930 0.010393739 0.000000000 0 0.0108
## [26,] -0.000413700815 0.006759402 0.000000000 0 0.0068
## [27,] -0.000583993114 0.006950099 0.000000000 0 0.0092
## [28,] -0.000864117404 0.010449808 0.000000000 0 0.0112
## [29,] -0.000066503782 0.005968716 0.000000000 0 0.0048
## [30,] -0.000170163209 0.004318929 0.000000000 0 0.0052
## [31,] -0.000189453818 0.003991600 0.000000000 0 0.0048
## [32,] -0.000364989861 0.006150400 0.000000000 0 0.0060
## [33,] -0.001041262057 0.012940966 0.000000000 0 0.0112
## [34,] -0.000471552169 0.008887122 0.000000000 0 0.0084
## [35,] -0.000348259672 0.006357364 0.000000000 0 0.0048
## [36,] -0.000214270045 0.004322548 0.000000000 0 0.0040
## [37,] -0.001883444729 0.017048341 0.000000000 0 0.0156
## [38,] -0.000371678917 0.006050061 0.000000000 0 0.0056
## [39,] -0.000119103273 0.008205004 0.000000000 0 0.0056
## [40,] -0.000229014558 0.003888444 0.000000000 0 0.0048
## [41,] -0.000252044262 0.006048754 0.000000000 0 0.0044
## [42,] -0.000223354995 0.005612090 0.000000000 0 0.0052
## [43,] 0.000212518611 0.010866769 0.000000000 0 0.0076
## [44,] -0.001279899659 0.015969309 0.000000000 0 0.0100
## [45,] -0.000803264264 0.011559414 0.000000000 0 0.0092
## [46,] -0.000367945543 0.007009637 0.000000000 0 0.0052
## [47,] -0.000536520982 0.008730588 0.000000000 0 0.0056
## [48,] -0.000712399238 0.009685180 0.000000000 0 0.0080
## [49,] -0.000161425498 0.007772472 0.000000000 0 0.0040
## [50,] -0.001090586982 0.015252794 0.000000000 0 0.0108
## [51,] -0.000756738730 0.012137244 0.000000000 0 0.0080
## [52,] -0.000701395263 0.010527526 0.000000000 0 0.0080
## [53,] -0.000542225668 0.008111342 0.000000000 0 0.0064
## [54,] -0.000853230359 0.011073983 0.000000000 0 0.0096
## [55,] 0.000136226048 0.007197069 0.000000000 0 0.0056
## [56,] -0.000036605044 0.001851556 0.000000000 0 0.0020
## [57,] -0.000117341855 0.003826224 0.000000000 0 0.0036
## [58,] -0.000165992032 0.003111426 0.000000000 0 0.0040
## [59,] -0.000289220494 0.006124989 0.000000000 0 0.0044
## [60,] -0.000164722849 0.003348375 0.000000000 0 0.0044
## [61,] -0.000766508478 0.010960191 0.000000000 0 0.0088
## [62,] -0.001718436446 0.016793540 0.000000000 0 0.0156
## [63,] -0.002625839237 0.020711075 0.000000000 0 0.0220
## [64,] -0.000301717388 0.005893842 0.000000000 0 0.0048
## [65,] -0.000288801444 0.006120300 0.000000000 0 0.0032
## [66,] -0.001078473377 0.015974588 0.000000000 0 0.0088
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## [622,] -0.001324412450 0.014263584 0.000000000 0 0.0152
## [623,] -0.000560012642 0.010428809 0.000000000 0 0.0084
## [624,] -0.001017123517 0.012908475 0.000000000 0 0.0096
## [625,] -0.000903764096 0.012843809 0.000000000 0 0.0100
## [626,] -0.000909749277 0.012686389 0.000000000 0 0.0112
## [627,] -0.000132577527 0.006061551 0.000000000 0 0.0060
## [628,] -0.003355496395 0.049421198 0.000000000 0 0.0164
## [629,] -0.000926762669 0.013299958 0.000000000 0 0.0116
## [630,] -0.000914038090 0.013886648 0.000000000 0 0.0096
## [631,] -0.000644291797 0.009580589 0.000000000 0 0.0076
## [632,] -0.002165540128 0.022071391 0.000000000 0 0.0156
## [633,] -0.001324075494 0.015517200 0.000000000 0 0.0140
## [634,] 0.000034985623 0.017421687 0.000000000 0 0.0068
## [635,] -0.000575394672 0.011133631 0.000000000 0 0.0072
## [636,] -0.002664580589 0.026807377 0.000000000 0 0.0152
## [637,] -0.000510186085 0.008031330 0.000000000 0 0.0096
## [638,] -0.000763531779 0.009113382 0.000000000 0 0.0092
## [639,] -0.000849372656 0.011834008 0.000000000 0 0.0092
## [640,] -0.001527857870 0.017832980 0.000000000 0 0.0124
## [641,] -0.000527503604 0.011180146 0.000000000 0 0.0080
## [642,] -0.000581529731 0.007163633 0.000000000 0 0.0096
## [643,] -0.000624440986 0.009563695 0.000000000 0 0.0080
## [644,] -0.001319846769 0.022909481 0.000000000 0 0.0112
## [645,] -0.001199608038 0.014915605 0.000000000 0 0.0100
## [646,] -0.000699012018 0.011857533 0.000000000 0 0.0056
## [647,] -0.000569431070 0.008176111 0.000000000 0 0.0080
## [648,] -0.001901123990 0.018309208 0.000000000 0 0.0148
## [649,] -0.001304170178 0.014229511 0.000000000 0 0.0148
## [650,] -0.000664581489 0.010923451 0.000000000 0 0.0072
## [651,] -0.003088401033 0.029030688 0.000000000 0 0.0176
## [652,] -0.001739302165 0.020101328 0.000000000 0 0.0124
## [653,] -0.000416112616 0.008469129 0.000000000 0 0.0068
## [654,] -0.000544329669 0.010832385 0.000000000 0 0.0068
## [655,] -0.000473985973 0.007364331 0.000000000 0 0.0060
## [656,] -0.000394011762 0.007090003 0.000000000 0 0.0064
## [657,] -0.000435116764 0.007934774 0.000000000 0 0.0056
## [658,] -0.001163813879 0.014134053 0.000000000 0 0.0128
## [659,] -0.000577922788 0.010281590 0.000000000 0 0.0092
## [660,] -0.001085381657 0.013179701 0.000000000 0 0.0100
## [661,] 0.000680647181 0.032562419 0.000000000 0 0.0092
## [662,] -0.000513777557 0.007786526 0.000000000 0 0.0076
## [663,] -0.001204616672 0.015391938 0.000000000 0 0.0100
## [664,] -0.000394294193 0.007145708 0.000000000 0 0.0072
## [665,] -0.000780183989 0.011746811 0.000000000 0 0.0068
## [666,] -0.000137846973 0.009613323 0.000000000 0 0.0068
## [667,] -0.000794393036 0.010563236 0.000000000 0 0.0092
## [668,] -0.000421507949 0.008700923 0.000000000 0 0.0076
## [669,] -0.000730749580 0.010924732 0.000000000 0 0.0068
## [670,] -0.000537917335 0.009223214 0.000000000 0 0.0072
## [671,] -0.001958481117 0.036191454 0.000000000 0 0.0116
## [672,] -0.000718161398 0.009996088 0.000000000 0 0.0088
## [673,] -0.000626035548 0.009919222 0.000000000 0 0.0100
## [674,] -0.000372587252 0.008695753 0.000000000 0 0.0056
## [675,] -0.000149203703 0.007183923 0.000000000 0 0.0064
## [676,] -0.000833097955 0.012832621 0.000000000 0 0.0096
## [677,] -0.000625209840 0.012795769 0.000000000 0 0.0080
## [678,] -0.001521342721 0.017961143 0.000000000 0 0.0112
## [679,] -0.001558532637 0.020233226 0.000000000 0 0.0140
## [680,] -0.000327036457 0.014040691 0.000000000 0 0.0064
## [681,] -0.000270399548 0.008051421 0.000000000 0 0.0060
## [682,] -0.001250793161 0.015916474 0.000000000 0 0.0104
## [683,] -0.001342914113 0.016352512 0.000000000 0 0.0108
## [684,] -0.000835891110 0.014226527 0.000000000 0 0.0068
## [685,] -0.001299778994 0.018951716 0.000000000 0 0.0088
## [686,] -0.000803979336 0.013422881 0.000000000 0 0.0080
## [687,] -0.000836207277 0.013457492 0.000000000 0 0.0076
## [688,] -0.000220066126 0.010041542 0.000000000 0 0.0056
## [689,] -0.000318971870 0.006644023 0.000000000 0 0.0060
## [690,] -0.001350612074 0.016579808 0.000000000 0 0.0112
## [691,] -0.000519060763 0.018652827 0.000000000 0 0.0084
## [692,] -0.001587947868 0.019732748 0.000000000 0 0.0116
## [693,] -0.000998190727 0.014113425 0.000000000 0 0.0128
## [694,] -0.001124465902 0.014207001 0.000000000 0 0.0096
## [695,] -0.000387307293 0.006318189 0.000000000 0 0.0044
## [696,] -0.001323131529 0.014070725 0.000000000 0 0.0132
## [697,] -0.000408633146 0.007062669 0.000000000 0 0.0076
## [698,] -0.000974316003 0.016531763 0.000000000 0 0.0068
## [699,] -0.000774622017 0.011352796 0.000000000 0 0.0096
## [700,] -0.002212975406 0.021648956 0.000000000 0 0.0164
## [701,] -0.000982937410 0.012643314 0.000000000 0 0.0092
## [702,] -0.002277843006 0.025129725 0.000000000 0 0.0152
## [703,] -0.003322910152 0.029006182 0.000000000 0 0.0192
## [704,] -0.000569439372 0.010626810 0.000000000 0 0.0088
## [705,] -0.001387367401 0.015078211 0.000000000 0 0.0136
## [706,] -0.001231921863 0.016324356 0.000000000 0 0.0108
## [707,] -0.000611374148 0.008170735 0.000000000 0 0.0076
## [708,] -0.000759857913 0.010703034 0.000000000 0 0.0076
## [709,] -0.000900980439 0.012654887 0.000000000 0 0.0088
## [710,] -0.001757922248 0.019235227 0.000000000 0 0.0128
## [711,] -0.000588101871 0.010188308 0.000000000 0 0.0068
## [712,] -0.000290507757 0.006254415 0.000000000 0 0.0068
## [713,] -0.001063737568 0.016027229 0.000000000 0 0.0088
## [714,] -0.000935887484 0.012249577 0.000000000 0 0.0088
## [715,] -0.000394520996 0.008274681 0.000000000 0 0.0056
## [716,] -0.000151695400 0.015859241 0.000000000 0 0.0076
## [717,] -0.002763723722 0.028074895 0.000000000 0 0.0164
## [718,] 0.000401801112 0.023167887 0.000000000 0 0.0056
## [719,] -0.001129521719 0.013565268 0.000000000 0 0.0128
## [720,] -0.000546422994 0.009201072 0.000000000 0 0.0076
## [721,] -0.000980097985 0.013118434 0.000000000 0 0.0092
## [722,] -0.000551255727 0.009679981 0.000000000 0 0.0056
## [723,] -0.001456317038 0.016586021 0.000000000 0 0.0116
## [724,] -0.000521684937 0.008555513 0.000000000 0 0.0076
## [725,] -0.002050698774 0.028057492 0.000000000 0 0.0112
## [726,] -0.001322914727 0.016443188 0.000000000 0 0.0108
## [727,] -0.000235417818 0.005926543 0.000000000 0 0.0060
## [728,] -0.001057126308 0.015723877 0.000000000 0 0.0084
## [729,] -0.001254607816 0.015663196 0.000000000 0 0.0132
## [730,] -0.001377979462 0.015254448 0.000000000 0 0.01445 Linear models for each predictor
5.1 Screening the exposures
None of the exposures had a PIP > 0.5. Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(adiposity ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Adiposity.csv"))5.2 Linear model for distance to waste sites
lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))
ad_waste_lm <- lm(adiposity ~ dist_m_waste_site +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male + days_to_peapod,
data = lm_df)
summary(ad_waste_lm)##
## Call:
## lm(formula = adiposity ~ dist_m_waste_site + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.1152 -2.6385 -0.1678 2.7592 15.5462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.02150 3.90254 2.568 0.0104 *
## dist_m_waste_site 0.36281 0.15149 2.395 0.0169 *
## lat 12.72052 148.21325 0.086 0.9316
## lon -5.73270 70.63195 -0.081 0.9353
## lat_lon_int 15.09494 178.21522 0.085 0.9325
## latina_re -0.48057 0.40192 -1.196 0.2322
## black_re -0.27689 0.43874 -0.631 0.5282
## other_re -0.87609 0.57642 -1.520 0.1290
## ed_no_hs 1.23866 0.65067 1.904 0.0573 .
## ed_hs 1.07560 0.58154 1.850 0.0648 .
## ed_aa 0.81041 0.51063 1.587 0.1129
## ed_4yr 0.07400 0.42583 0.174 0.8621
## low_bmi -0.42315 0.80718 -0.524 0.6003
## ovwt_bmi 0.52044 0.34122 1.525 0.1276
## obese_bmi 1.24425 0.38806 3.206 0.0014 **
## concep_spring 0.29517 0.39971 0.738 0.4605
## concep_summer 0.13378 0.39414 0.339 0.7344
## concep_fall 0.03868 0.39069 0.099 0.9212
## concep_2010 -0.55100 3.90233 -0.141 0.8878
## concep_2011 -1.11020 3.90475 -0.284 0.7762
## concep_2012 -1.36997 3.89964 -0.351 0.7255
## concep_2013 -1.04232 3.90481 -0.267 0.7896
## maternal_age 0.79576 0.18829 4.226 0.00002669215 ***
## any_smoker -0.88965 0.53394 -1.666 0.0961 .
## smokeSH -0.09976 0.37929 -0.263 0.7926
## mean_cpss -0.06078 0.16639 -0.365 0.7150
## mean_epsd -0.19513 0.16928 -1.153 0.2494
## male -1.37099 0.27394 -5.005 0.00000069768 ***
## days_to_peapod 0.82688 0.13914 5.943 0.00000000429 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.773 on 751 degrees of freedom
## Multiple R-squared: 0.1402, Adjusted R-squared: 0.1082
## F-statistic: 4.375 on 28 and 751 DF, p-value: 0.000000000001403plot(ad_waste_lm)
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
5.3 Linear model for respiratory hospitalization rates
lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))
ad_res_lm <- lm(adiposity ~ res_rate_adj +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male + days_to_peapod,
data = lm_df)
summary(ad_res_lm)##
## Call:
## lm(formula = adiposity ~ res_rate_adj + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.7234 -2.5753 -0.2042 2.7269 16.1631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.67278 3.90877 2.475 0.01356 *
## res_rate_adj -0.24964 0.15140 -1.649 0.09960 .
## lat 36.76972 148.72945 0.247 0.80480
## lon -17.28087 70.88017 -0.244 0.80745
## lat_lon_int 44.14802 178.83348 0.247 0.80508
## latina_re -0.38383 0.40356 -0.951 0.34185
## black_re -0.19174 0.43981 -0.436 0.66298
## other_re -0.81865 0.57851 -1.415 0.15746
## ed_no_hs 1.31937 0.65663 2.009 0.04486 *
## ed_hs 1.15845 0.58646 1.975 0.04860 *
## ed_aa 0.94161 0.51282 1.836 0.06673 .
## ed_4yr 0.13362 0.42564 0.314 0.75367
## low_bmi -0.50970 0.80895 -0.630 0.52884
## ovwt_bmi 0.47288 0.34205 1.382 0.16723
## obese_bmi 1.26674 0.38909 3.256 0.00118 **
## concep_spring 0.31816 0.40032 0.795 0.42700
## concep_summer 0.11014 0.39513 0.279 0.78053
## concep_fall 0.04729 0.39147 0.121 0.90387
## concep_2010 -0.33604 3.90881 -0.086 0.93151
## concep_2011 -0.86851 3.91105 -0.222 0.82432
## concep_2012 -1.16914 3.90637 -0.299 0.76480
## concep_2013 -0.83812 3.91148 -0.214 0.83039
## maternal_age 0.76831 0.18806 4.086 0.00004870493 ***
## any_smoker -0.86685 0.53535 -1.619 0.10582
## smokeSH -0.09518 0.38007 -0.250 0.80233
## mean_cpss -0.04247 0.16639 -0.255 0.79861
## mean_epsd -0.19821 0.16980 -1.167 0.24346
## male -1.32203 0.27511 -4.805 0.00000186532 ***
## days_to_peapod 0.82938 0.13942 5.949 0.00000000414 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.781 on 751 degrees of freedom
## Multiple R-squared: 0.1368, Adjusted R-squared: 0.1046
## F-statistic: 4.251 on 28 and 751 DF, p-value: 0.000000000004589plot(ad_res_lm)
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
5.4 Linear model for property crime rates
lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))
ad_pcrime_lm <- lm(adiposity ~ property_crime_rate +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male + days_to_peapod,
data = lm_df)
summary(ad_pcrime_lm)##
## Call:
## lm(formula = adiposity ~ property_crime_rate + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6783 -2.6161 -0.1684 2.7626 15.8124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.65291 3.90266 2.473 0.01360 *
## property_crime_rate -0.31479 0.13972 -2.253 0.02455 *
## lat 31.91270 148.29287 0.215 0.82967
## lon -14.93929 70.67019 -0.211 0.83264
## lat_lon_int 38.29701 178.30884 0.215 0.83000
## latina_re -0.46827 0.40192 -1.165 0.24435
## black_re -0.29343 0.43940 -0.668 0.50446
## other_re -0.93457 0.57731 -1.619 0.10590
## ed_no_hs 1.19286 0.65058 1.834 0.06712 .
## ed_hs 1.07542 0.58181 1.848 0.06494 .
## ed_aa 0.91635 0.51063 1.795 0.07313 .
## ed_4yr 0.18710 0.42523 0.440 0.66007
## low_bmi -0.46686 0.80730 -0.578 0.56324
## ovwt_bmi 0.46817 0.34145 1.371 0.17074
## obese_bmi 1.25965 0.38829 3.244 0.00123 **
## concep_spring 0.32470 0.39966 0.812 0.41680
## concep_summer 0.14151 0.39434 0.359 0.71980
## concep_fall 0.02365 0.39096 0.060 0.95179
## concep_2010 -0.18066 3.90305 -0.046 0.96309
## concep_2011 -0.71684 3.90537 -0.184 0.85441
## concep_2012 -1.03992 3.90058 -0.267 0.78984
## concep_2013 -0.72418 3.90556 -0.185 0.85295
## maternal_age 0.77043 0.18770 4.104 0.00004496165 ***
## any_smoker -0.86307 0.53440 -1.615 0.10672
## smokeSH -0.10116 0.37946 -0.267 0.78985
## mean_cpss -0.03802 0.16586 -0.229 0.81874
## mean_epsd -0.20551 0.16917 -1.215 0.22481
## male -1.40426 0.27486 -5.109 0.00000041128 ***
## days_to_peapod 0.82385 0.13921 5.918 0.00000000495 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.775 on 751 degrees of freedom
## Multiple R-squared: 0.1395, Adjusted R-squared: 0.1074
## F-statistic: 4.348 on 28 and 751 DF, p-value: 0.000000000001819plot(ad_pcrime_lm)## Warning: not plotting observations with leverage one:
## 1
5.5 Linear model for %unemployed rates
lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))
ad_unemp_lm <- lm(adiposity ~ pct_unemp +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male + days_to_peapod,
data = lm_df)
summary(ad_unemp_lm)##
## Call:
## lm(formula = adiposity ~ pct_unemp + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6136 -2.5739 -0.1227 2.6643 15.9796
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.66018 3.90718 2.472 0.013641 *
## pct_unemp -0.27813 0.15209 -1.829 0.067843 .
## lat 18.84591 148.40739 0.127 0.898984
## lon -8.68304 70.72418 -0.123 0.902319
## lat_lon_int 22.61179 178.44698 0.127 0.899200
## latina_re -0.29709 0.40929 -0.726 0.468151
## black_re -0.09939 0.44480 -0.223 0.823243
## other_re -0.80122 0.57866 -1.385 0.166583
## ed_no_hs 1.32492 0.65577 2.020 0.043695 *
## ed_hs 1.19286 0.58775 2.030 0.042755 *
## ed_aa 0.97771 0.51414 1.902 0.057602 .
## ed_4yr 0.19854 0.42625 0.466 0.641502
## low_bmi -0.41917 0.80868 -0.518 0.604377
## ovwt_bmi 0.48223 0.34170 1.411 0.158581
## obese_bmi 1.29104 0.38955 3.314 0.000963 ***
## concep_spring 0.29460 0.40051 0.736 0.462232
## concep_summer 0.11011 0.39493 0.279 0.780471
## concep_fall 0.04963 0.39131 0.127 0.899106
## concep_2010 -0.39542 3.90747 -0.101 0.919421
## concep_2011 -0.91640 3.90959 -0.234 0.814740
## concep_2012 -1.21936 3.90492 -0.312 0.754928
## concep_2013 -0.85571 3.90990 -0.219 0.826821
## maternal_age 0.74830 0.18780 3.985 0.00007418007 ***
## any_smoker -0.93043 0.53505 -1.739 0.082455 .
## smokeSH -0.08158 0.38005 -0.215 0.830094
## mean_cpss -0.03983 0.16616 -0.240 0.810619
## mean_epsd -0.19942 0.16960 -1.176 0.240031
## male -1.35414 0.27429 -4.937 0.00000097868 ***
## days_to_peapod 0.83228 0.13939 5.971 0.00000000364 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.779 on 751 degrees of freedom
## Multiple R-squared: 0.1375, Adjusted R-squared: 0.1054
## F-statistic: 4.277 on 28 and 751 DF, p-value: 0.000000000003591plot(ad_unemp_lm)## Warning: not plotting observations with leverage one:
## 1
